Journal of Biostatistics and Epidemiology
|
|
- Virginia Norman
- 5 years ago
- Views:
Transcription
1 Journal of Biostatistics and Epidemiology Original Article Robust correlation coefficient goodness-of-fit test for the Gumbel distribution Abbas Mahdavi 1* 1 Department of Statistics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran ARTICLE INFO ABSTRACT Received Revised Accepted Published Key words: Outlier; Regression analysis; Statistical distributions Background & Aim: A single outlier can even have a large disturbing effect on a classical statistical method that is optimal under the classical assumptions. One of the powerful goodness-offit tests is the correlation coefficient test, however this test suffers from the presence of outliers. Methods & Materials: This study provides a simple robust method for test of goodness of fit for the Gumbel distribution [extreme value distribution (EVD) type I family] through using the new diagnostic tool called the Forward Search (FS) method. The FS version of this test was introduce in the present study, which is not affected by the outliers. Results: A new robust method for testing the goodness-of-fit for Gumbel distribution has been presented. The approach gives information about the distribution of majority of the data and the percentage of contamination. Conclusion: A new robust method for testing the goodness-of-fit for the Gumbel distribution has been presented. The simple and fast method have been used to find distribution of proposed statistic. In addition, using the transformation study, an application to the two-parameter Weibull distribution has been investigated. The performance and the ability of this procedure to capture the structure of data have been illustrated by some simulation studies. Introduction 1 The extreme value distributions (EVDs) are widely used in risk management, finance, insurance, economics, hydrology, material sciences, telecommunications, and many other industries dealing with extreme events. The EVD arises from the Fisher-Tippett limit theorem (1) on extreme values or maxima in sample data. Let X 1, X 2,, X n be independent and identically distributed (IID) random variables and M n =max(x 1,X 2,,X n ). If there exist constants and, and some nondegenerate distribution function G, such that, * Corresponding Author: Abbas Mahdavi, Postal Address: Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. a.mahdavi@vru.ac.ir then, G belongs to one of the three types of EVDs: Fréchet, Weibull, and Gumbel. These can be grouped into the generalized EVD. In this study, it has been tried to propose a robust goodness-of-fit test for Gumbel (Type I EVD) distribution. The assumptions of such models should be validated before progressing with other aspects of statistical inference. In practice, it often happens that such assumptions hold approximately in majority of observations, however some observations follow a different pattern or no pattern at all. Such atypical data are called outliers. A single outlier can even have a large disturbing effect on a classical statistical method that is optimal under the classical assumptions. One of the basic tools useful for this purpose is the correlation coefficient goodness-of-fit test based on Please cite this article in press as: Mahdavi A. Robust correlation coefficient goodness-of-fit test for the Gumbel distribution. J Biostat Epidemiol. 2018; 4(1):
2 Robust goodness-of-fit test for Gumbel quantile-quantile (QQ) plot. The objective in this study was to adopt the Forward Search (FS) method in the goodness of Gumbel distribution. Correlation coefficient test is one of the powerful tests introduced by Filliben (2) to test normality. Kinnison (3) assessed the goodness of fit of EVD type-i based on Filliben s correlation coefficient test and examined its power properties for various alternative models. The correlation coefficient statistic is not a robust statistic and hence, the presence of outliers influences this test strongly. The test involves computing the correlation coefficient between the ranked data and the expected value of the order statistic with the same rank. In this study, it has been tried to determine how many and which observations agree with the hypothesis of Gumbel distribution and also as an application for testing the goodness of fit for Weibull distribution. The FS approach is a powerful general method providing diagnostic plots for finding outliers and discovering their underlying effects on models fitted to the data and for assessing the adequacy of the model. Riani and Atkinson (4) and Atkinson and Riani (5, 6) developed the FS procedure for regression modeling and multivariate analysis frameworks. The FS method starts from a small, robustly chosen subset of the data. The method increases the subset size using some measures of closeness from fitted model until finally all the data are fitted. The outliers enter the model in the last steps and the entrance point of the outliers can be revealed through monitoring some statistics of interest during the process. Recently, the FS method has been implemented in wide applications, for example, analysis of variance (ANOVA) framework (7), testing normality (8), testing the parameters of a normal population (9), and density estimation of a unimodal continuous distribution (10). The study be Atkinson et al. (11) can be referred to for further results. Methods Correlation coefficient goodness-of-fit test for Gumbel distribution: The correlation coefficient test was introduced by Filliben (2) to test goodness of fit for the normal distribution. Kinnison (3) assessed the goodness of fit of EVD type-i based on Filliben s correlation coefficient test and examined its power properties for various alternative models. A QQ plot is a common and basic technique used for finding a suitable data model. When comparing an observed data to a hypothesized distribution, the plot of the ordered observations versus the appropriate quantiles of assumed distribution should look approximately linear and hence the product moment correlation coefficient (PMCC), which measures the degree of linear association between two random variables, is an appropriate test statistic. The correlation coefficient goodness-of-fit test for the Gumbel distribution is built as follows. Let X be a random variable from the Type I family distribution. ( * +) ;, (1) Where, µ and are unknown location and scale parameters, respectively. In such locationscale model, there is a simple relationship between the p-quantiles of X and W=(X-µ)/σis the standard Gumbel variable (µ = 0, σ = 1). The p-quantile of X, defined by P(X x p ) = p, is (2) Thus, x p is a linear function of, the p-quantile of W. Let (X (1),X (2),,X (n) ) be an ordered sample of size n from X, for appropriate p i ;i=1,2, n (the plotting positions), x pi can be approximated by the i-th order sample X (i) Thus the correlation coefficient statistic, R, for goodness-of-fit test is defined as the correlation between ordered sample X (i) and the p i -quantile of W, W pi. Many plotting positions have been proposed in the literature; in this study, the median rank was used due to its robustness property and was therefore used in the case of skewed distributions, like the EVD (12, 13). The median rank, m (i), of the i-th order statistics is given by (3) Where, b 0.5,α,β is the median of the beta distribution with parameters α and β. 31
3 Robust goodness-of-fit test for Gumbel The distribution of R can be estimated by means of Monte Carlo simulation for different sample sizes. The hypothesized distribution (1) is rejected if the observed value of R is smaller than the critical value. As an application, in order to use the correlation coefficient test for testing the validity of two-parameter Weibull distribution to the data with cumulative distribution function (CDF): * ( ) +;. (4) The two-parameter Weibull distribution can be transformed to the family of two-parameter Gumbel distribution using a logarithmic transformation. It is necessary to transform into a Gumbel distribution with location parameter µ = log(β) and scale parameter σ =1/α by taking the logarithm of the data. FS in correlation coefficient goodness-of-fit test for the Gumbel distribution: Let x (.) = (x (1), x (2),,x (n) ). The vector of ordered observations comes from a Gumbel distribution (1), then it is possible to write, (5) Where, w mi = log(-log( mi )), and m i is the median rank defined in (3). In this section, the FS method introduced by Atkinson and Riani (5) was used to analyze the behavior of regression model. The FS method is a powerful approach not only to detect outliers, but also to investigate their effects on the estimation of parameters and on aspects of inference about models. The basic idea of the FS approach was to order the observations by their proximity to the fitted model. The FS method was made up of the following three main steps: the starting point was to find the appropriate starting subset of observations, the second step presented the plan to progress in FS, and the last step was to monitor some suitable quantities during the search. In the following subsections, how these three points are performed will be described. Step 1: Choice of the initial subset: Starting point of the FS procedure was to choose outlier free subset of observations robustly. To start the FS approach, the size of initial subset had to be specified. This size could be as small as p = 2. Therefore, the search was performed over subsets of P observations to find the best subset of observations. The initial subset could be achieved by the use of robust regression estimator least median of squares (LMS) regression estimator proposed by Rousseeuw (14). Step 2: Progressing in the search: At each step of the search, the procedure added to the subset the observation that was closest to the previously fitted model. Let S (k) be a subset of size k, the FS moves to S (k+1) in the following way: after the least square regression model is fitted to the S (k) subset, all observations are ordered according to their square residuals, now the k + 1 observations are chosen with the smallest square residuals. This procedure is repeated until all observations are entered into the model. Step 3: Monitoring the search: For detecting and determining the effect of outliers, some statistics of interest must be monitored during the search. The FS version of correlation coefficient, R FS, is defined as a collection of R (correlation coefficient) statistics computed for different subsets of X (.) and corresponding units of w mi. Let k w (k) w be the units of w mi corresponding to the subset S (k), then the R FS is defined as (6). The empirical quantiles of (6) during the search can be estimated by simulation in each step of the search. In any step of the search, the acceptance region lies between the value of the chosen quantile and 1. Results Simulation study: In order to evaluate the proposed procedure, simulation studies were conducted with the aim to consider the behavior of statistic (6) in the presence of outliers and ability of FS to detect them. Consider 6 samples were generated in the following way: Sample A: 100 observations were generated from a standard Gumbel distribution. Sample B: 95 observations were generated from a standard Gumbel distribution and for 32
4 Robust goodness-of-fit test for Gumbel A B C D E F Figure 1. Forward plots of R forward search (R FS ) during the search for samples A-F. Sample C: 95 observations were generated from a standard Gumbel distribution and for Sample D: 100 observations were generated Sample E: 95 observations were generated from a and for Sample F: 95 observations were generated from a and for In Figure 1, the values of R FS during the search have been plotted for samples A-F and compared with estimated corresponding 5% quantile (dashed line) of its distribution obtained from ordered observations method discussed in the next section. The null hypothesis of Gumbel distribution was accepted in each step of the search for clean sample A and it was rejected after entrance of outliers in the last steps (step 96 onwards) for contaminated samples B and C, indicating 5 observations were outliers. Moreover, the same results for samples D-F were summarized as follows: the null hypothesis of two-parameter Weibull distribution was accepted in any step of the search for clean sample D and it was rejected from step 96 onwards for samples E and F. Discussion The empirical null distribution of (6) can be found by simulating numerous samples generated from a standard Gumbel distribution. Since the FS is a reiterative algorithm, this way of estimating distribution is very time consuming. Atkinson and Riani (15) proposed the method of ordered observations to estimate the distribution of outlier test statistic. In the following subsection, this simple and fast method will be described briefly. Method of ordered observations: The FS orders all observations in each steps of the search. In the absence of outliers, when moving from S (k) to S (k+1), most of the time, only one new observation joins the subset and this ordering does not change much during the search. Hence, the observations can be ordered only once according to square residuals resulting from the chosen initial subset, denoted by X (ord). In the step k of the search, only the first k observations of X (ord) are chosen. 33
5 Correlation coefficient Correlation coefficient Robust goodness-of-fit test for Gumbel Figure 2. 5% bounds of the empirical distribution (continuous lines) and the estimated distribution using the ordered observations method (dashed lines) for sample sizes n = 50 (left panel) and n = 100 (right panel) Figure 2 shows the 5% bounds of the empirical distribution and the estimated distribution using the ordered observations method for sample sizes n = 50 and n = 100. The analysis of figure 2 indicates that the method of ordered observations approximate the 5% quantile of (6) very well except the middle of the search and by increasing the sample size, this approximation was improved. To specify the acceptance region, the lower bounds of (6) are required and hence, only the 5% quantile of (6) was curved in figure 2. Conclusion In this study, a new robust method has been presented to test the goodness-of-fit for Gumbel distribution. The approach provides information on the distribution of majority of the data and the percentage of contamination. At every step of the FS, the proposed statistic was computed and a cut-off point divided the group of outliers from the other observations with a graphical approach. In order to illustrate the application and the advantage of the FS approach, some artificial examples were used. In addition, the simple and fast method was used to find distribution of the proposed statistic. Furthermore, an application of the proposed approach to the goodness-of-fit test was shown for the two-parameter Weibull distribution. Conflict of Interests Authors have no conflict of interests. Acknowledgments This study was supported by the research council of Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran. References 1. Fisher RA, Caleb Tippett LH. Limiting forms of the frequency distribution of the largest or smallest member of a sample. Mathematical Proceedings of the Cambridge Philosophical Society 1928; 24(2): Filliben JJ. The probability plot correlation coefficient test for normality. Technometrics 1975; 17(1): Kinnison R. Correlation coefficient goodness-of-fit test for the extreme-value distribution. Am Stat 1989; 43(2): Riani M, Atkinson AC. Robust diagnostic data analysis: Transformations in regression. Technometrics 2000; 42(4): Atkinson AC, Riani M. Forward search added-variable t-tests and the effect of masked outliers on model selection. Biometrika 2002; 89(4):
6 Robust goodness-of-fit test for Gumbel 6. Atkinson AC, Riani M. The forward search and data visualisation. Comput Stat 2004; 19(1): Bertaccini B, Varriale R. Robust analysis of variance: An approach based on the forward search. Comput Stat Data Anal 2006; 51(10): Coin D. Statistical methods and applications. Stat Methods Appt 2008; 17(1): Mahdavi A, Towhidi M. Robust tests for testing the parameters of a normal population. Journal of Sciences, Islamic Republic of Iran 2014; 25(3): Mahdavi A, Towhidi M. Density estimation of a unimodal continuous distribution in the presence of outliers. Iranian Journal of Science and Technology, Transactions A: Science 2017; Atkinson AC, Riani M, Cerioli A. The forward search: Theory and data analysis. J Korean Stat Soc 2010; 39(2): D'Agostino RB. Goodness-of-fit-techniques. Boca Raton, FL: CRC Press; Castillo E, Hadi AS, Balakrishnan N, Sarabia JM. Extreme value and related models with applications in engineering and science. Hoboken, NJ: Wiley; Rousseeuw PJ. Least median of squares regression. J Am Stat Assoc 1984; 79(388): Atkinson AC, Riani M. Distribution theory and simulations for tests of outliers in regression. J Comput Graph Stat 2006; 15(2):
Accurate and Powerful Multivariate Outlier Detection
Int. Statistical Inst.: Proc. 58th World Statistical Congress, 11, Dublin (Session CPS66) p.568 Accurate and Powerful Multivariate Outlier Detection Cerioli, Andrea Università di Parma, Dipartimento di
More informationMonitoring Random Start Forward Searches for Multivariate Data
Monitoring Random Start Forward Searches for Multivariate Data Anthony C. Atkinson 1, Marco Riani 2, and Andrea Cerioli 2 1 Department of Statistics, London School of Economics London WC2A 2AE, UK, a.c.atkinson@lse.ac.uk
More information401 Review. 6. Power analysis for one/two-sample hypothesis tests and for correlation analysis.
401 Review Major topics of the course 1. Univariate analysis 2. Bivariate analysis 3. Simple linear regression 4. Linear algebra 5. Multiple regression analysis Major analysis methods 1. Graphical analysis
More informationHomework 2: Simple Linear Regression
STAT 4385 Applied Regression Analysis Homework : Simple Linear Regression (Simple Linear Regression) Thirty (n = 30) College graduates who have recently entered the job market. For each student, the CGPA
More informationFrequency Analysis & Probability Plots
Note Packet #14 Frequency Analysis & Probability Plots CEE 3710 October 0, 017 Frequency Analysis Process by which engineers formulate magnitude of design events (i.e. 100 year flood) or assess risk associated
More informationThe Goodness-of-fit Test for Gumbel Distribution: A Comparative Study
MATEMATIKA, 2012, Volume 28, Number 1, 35 48 c Department of Mathematics, UTM. The Goodness-of-fit Test for Gumbel Distribution: A Comparative Study 1 Nahdiya Zainal Abidin, 2 Mohd Bakri Adam and 3 Habshah
More informationGlossary. The ISI glossary of statistical terms provides definitions in a number of different languages:
Glossary The ISI glossary of statistical terms provides definitions in a number of different languages: http://isi.cbs.nl/glossary/index.htm Adjusted r 2 Adjusted R squared measures the proportion of the
More informationModeling Extremal Events Is Not Easy: Why the Extreme Value Theorem Cannot Be As General As the Central Limit Theorem
University of Texas at El Paso DigitalCommons@UTEP Departmental Technical Reports (CS) Department of Computer Science 5-2015 Modeling Extremal Events Is Not Easy: Why the Extreme Value Theorem Cannot Be
More informationModified Kolmogorov-Smirnov Test of Goodness of Fit. Catalonia-BarcelonaTECH, Spain
152/304 CoDaWork 2017 Abbadia San Salvatore (IT) Modified Kolmogorov-Smirnov Test of Goodness of Fit G.S. Monti 1, G. Mateu-Figueras 2, M. I. Ortego 3, V. Pawlowsky-Glahn 2 and J. J. Egozcue 3 1 Department
More informationSimultaneous Concentration Bands for Continuous Random Samples
Worcester Polytechnic Institute Digital WPI Mathematical Sciences Faculty Publications Department of Mathematical Sciences 10-1-2004 Simultaneous Concentration Bands for Continuous Random Samples Balgobin
More informationIdentifying and accounting for outliers and extreme response patterns in latent variable modelling
Identifying and accounting for outliers and extreme response patterns in latent variable modelling Irini Moustaki Athens University of Economics and Business Outline 1. Define the problem of outliers and
More informationOverview of Extreme Value Analysis (EVA)
Overview of Extreme Value Analysis (EVA) Brian Reich North Carolina State University July 26, 2016 Rossbypalooza Chicago, IL Brian Reich Overview of Extreme Value Analysis (EVA) 1 / 24 Importance of extremes
More informationRobust Bayesian regression with the forward search: theory and data analysis
TEST (2017) 26:869 886 DOI 10.1007/s11749-017-0542-6 ORIGINAL PAPER Robust Bayesian regression with the forward search: theory and data analysis Anthony C. Atkinson 1 Aldo Corbellini 2 Marco Riani 2 Received:
More information* Tuesday 17 January :30-16:30 (2 hours) Recored on ESSE3 General introduction to the course.
Name of the course Statistical methods and data analysis Audience The course is intended for students of the first or second year of the Graduate School in Materials Engineering. The aim of the course
More informationMonte Carlo Studies. The response in a Monte Carlo study is a random variable.
Monte Carlo Studies The response in a Monte Carlo study is a random variable. The response in a Monte Carlo study has a variance that comes from the variance of the stochastic elements in the data-generating
More informationRegression Analysis for Data Containing Outliers and High Leverage Points
Alabama Journal of Mathematics 39 (2015) ISSN 2373-0404 Regression Analysis for Data Containing Outliers and High Leverage Points Asim Kumer Dey Department of Mathematics Lamar University Md. Amir Hossain
More informationEstimation of Gutenberg-Richter seismicity parameters for the Bundaberg region using piecewise extended Gumbel analysis
Estimation of Gutenberg-Richter seismicity parameters for the Bundaberg region using piecewise extended Gumbel analysis Abstract Mike Turnbull Central Queensland University The Gumbel statistics of extreme
More informationTwo-by-two ANOVA: Global and Graphical Comparisons Based on an Extension of the Shift Function
Journal of Data Science 7(2009), 459-468 Two-by-two ANOVA: Global and Graphical Comparisons Based on an Extension of the Shift Function Rand R. Wilcox University of Southern California Abstract: When comparing
More informationRobust Wilks' Statistic based on RMCD for One-Way Multivariate Analysis of Variance (MANOVA)
ISSN 2224-584 (Paper) ISSN 2225-522 (Online) Vol.7, No.2, 27 Robust Wils' Statistic based on RMCD for One-Way Multivariate Analysis of Variance (MANOVA) Abdullah A. Ameen and Osama H. Abbas Department
More informationROBUSTNESS OF TWO-PHASE REGRESSION TESTS
REVSTAT Statistical Journal Volume 3, Number 1, June 2005, 1 18 ROBUSTNESS OF TWO-PHASE REGRESSION TESTS Authors: Carlos A.R. Diniz Departamento de Estatística, Universidade Federal de São Carlos, São
More informationHANDBOOK OF APPLICABLE MATHEMATICS
HANDBOOK OF APPLICABLE MATHEMATICS Chief Editor: Walter Ledermann Volume VI: Statistics PART A Edited by Emlyn Lloyd University of Lancaster A Wiley-Interscience Publication JOHN WILEY & SONS Chichester
More informationContents. Acknowledgments. xix
Table of Preface Acknowledgments page xv xix 1 Introduction 1 The Role of the Computer in Data Analysis 1 Statistics: Descriptive and Inferential 2 Variables and Constants 3 The Measurement of Variables
More informationA Monte Carlo Simulation of the Robust Rank- Order Test Under Various Population Symmetry Conditions
Journal of Modern Applied Statistical Methods Volume 12 Issue 1 Article 7 5-1-2013 A Monte Carlo Simulation of the Robust Rank- Order Test Under Various Population Symmetry Conditions William T. Mickelson
More informationSpatial autocorrelation: robustness of measures and tests
Spatial autocorrelation: robustness of measures and tests Marie Ernst and Gentiane Haesbroeck University of Liege London, December 14, 2015 Spatial Data Spatial data : geographical positions non spatial
More informationREFERENCES AND FURTHER STUDIES
REFERENCES AND FURTHER STUDIES by..0. on /0/. For personal use only.. Afifi, A. A., and Azen, S. P. (), Statistical Analysis A Computer Oriented Approach, Academic Press, New York.. Alvarez, A. R., Welter,
More informationUsing Simulation Procedure to Compare between Estimation Methods of Beta Distribution Parameters
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 6 (2017), pp. 2307-2324 Research India Publications http://www.ripublication.com Using Simulation Procedure to Compare between
More informationLeast Absolute Value vs. Least Squares Estimation and Inference Procedures in Regression Models with Asymmetric Error Distributions
Journal of Modern Applied Statistical Methods Volume 8 Issue 1 Article 13 5-1-2009 Least Absolute Value vs. Least Squares Estimation and Inference Procedures in Regression Models with Asymmetric Error
More informationTESTS FOR TRANSFORMATIONS AND ROBUST REGRESSION. Anthony Atkinson, 25th March 2014
TESTS FOR TRANSFORMATIONS AND ROBUST REGRESSION Anthony Atkinson, 25th March 2014 Joint work with Marco Riani, Parma Department of Statistics London School of Economics London WC2A 2AE, UK a.c.atkinson@lse.ac.uk
More informationAn Extended Weighted Exponential Distribution
Journal of Modern Applied Statistical Methods Volume 16 Issue 1 Article 17 5-1-017 An Extended Weighted Exponential Distribution Abbas Mahdavi Department of Statistics, Faculty of Mathematical Sciences,
More informationIntroduction to Robust Statistics. Anthony Atkinson, London School of Economics, UK Marco Riani, Univ. of Parma, Italy
Introduction to Robust Statistics Anthony Atkinson, London School of Economics, UK Marco Riani, Univ. of Parma, Italy Multivariate analysis Multivariate location and scatter Data where the observations
More informationIDENTIFYING MULTIPLE OUTLIERS IN LINEAR REGRESSION : ROBUST FIT AND CLUSTERING APPROACH
SESSION X : THEORY OF DEFORMATION ANALYSIS II IDENTIFYING MULTIPLE OUTLIERS IN LINEAR REGRESSION : ROBUST FIT AND CLUSTERING APPROACH Robiah Adnan 2 Halim Setan 3 Mohd Nor Mohamad Faculty of Science, Universiti
More informationRobust repeated median regression in moving windows with data-adaptive width selection SFB 823. Discussion Paper. Matthias Borowski, Roland Fried
SFB 823 Robust repeated median regression in moving windows with data-adaptive width selection Discussion Paper Matthias Borowski, Roland Fried Nr. 28/2011 Robust Repeated Median regression in moving
More informationTwo Weighted Distributions Generated by Exponential Distribution
Journal of Mathematical Extension Vol. 9, No. 1, (2015), 1-12 ISSN: 1735-8299 URL: http://www.ijmex.com Two Weighted Distributions Generated by Exponential Distribution A. Mahdavi Vali-e-Asr University
More informationStat 5101 Lecture Notes
Stat 5101 Lecture Notes Charles J. Geyer Copyright 1998, 1999, 2000, 2001 by Charles J. Geyer May 7, 2001 ii Stat 5101 (Geyer) Course Notes Contents 1 Random Variables and Change of Variables 1 1.1 Random
More informationPrediction of Bike Rental using Model Reuse Strategy
Prediction of Bike Rental using Model Reuse Strategy Arun Bala Subramaniyan and Rong Pan School of Computing, Informatics, Decision Systems Engineering, Arizona State University, Tempe, USA. {bsarun, rong.pan}@asu.edu
More informationSmall Sample Corrections for LTS and MCD
myjournal manuscript No. (will be inserted by the editor) Small Sample Corrections for LTS and MCD G. Pison, S. Van Aelst, and G. Willems Department of Mathematics and Computer Science, Universitaire Instelling
More informationTackling Statistical Uncertainty in Method Validation
Tackling Statistical Uncertainty in Method Validation Steven Walfish President, Statistical Outsourcing Services steven@statisticaloutsourcingservices.com 301-325 325-31293129 About the Speaker Mr. Steven
More informationLQ-Moments for Statistical Analysis of Extreme Events
Journal of Modern Applied Statistical Methods Volume 6 Issue Article 5--007 LQ-Moments for Statistical Analysis of Extreme Events Ani Shabri Universiti Teknologi Malaysia Abdul Aziz Jemain Universiti Kebangsaan
More informationJournal of Environmental Statistics
jes Journal of Environmental Statistics February 2010, Volume 1, Issue 3. http://www.jenvstat.org Exponentiated Gumbel Distribution for Estimation of Return Levels of Significant Wave Height Klara Persson
More informationSome Statistical Inferences For Two Frequency Distributions Arising In Bioinformatics
Applied Mathematics E-Notes, 14(2014), 151-160 c ISSN 1607-2510 Available free at mirror sites of http://www.math.nthu.edu.tw/ amen/ Some Statistical Inferences For Two Frequency Distributions Arising
More informationNew robust dynamic plots for regression mixture detection
Adv Data Anal Classif (2009) 3:263 279 DOI 10.1007/s11634-009-0050-y REGULAR ARTICLE New robust dynamic plots for regression mixture detection Domenico Perrotta Marco Riani Francesca Torti Received: 12
More informationTesting Goodness-of-Fit for Exponential Distribution Based on Cumulative Residual Entropy
This article was downloaded by: [Ferdowsi University] On: 16 April 212, At: 4:53 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 172954 Registered office: Mortimer
More informationIMPACT OF ALTERNATIVE DISTRIBUTIONS ON QUANTILE-QUANTILE NORMALITY PLOT
Colloquium Biometricum 45 2015, 67 78 IMPACT OF ALTERNATIVE DISTRIBUTIONS ON QUANTILE-QUANTILE NORMALITY PLOT Zofia Hanusz, Joanna Tarasińska Department of Applied Mathematics and Computer Science University
More informationFinancial Econometrics and Volatility Models Extreme Value Theory
Financial Econometrics and Volatility Models Extreme Value Theory Eric Zivot May 3, 2010 1 Lecture Outline Modeling Maxima and Worst Cases The Generalized Extreme Value Distribution Modeling Extremes Over
More informationDiagnostic Test for GARCH Models Based on Absolute Residual Autocorrelations
Diagnostic Test for GARCH Models Based on Absolute Residual Autocorrelations Farhat Iqbal Department of Statistics, University of Balochistan Quetta-Pakistan farhatiqb@gmail.com Abstract In this paper
More informationrobustness, efficiency, breakdown point, outliers, rank-based procedures, least absolute regression
Robust Statistics robustness, efficiency, breakdown point, outliers, rank-based procedures, least absolute regression University of California, San Diego Instructor: Ery Arias-Castro http://math.ucsd.edu/~eariasca/teaching.html
More informationReview. DS GA 1002 Statistical and Mathematical Models. Carlos Fernandez-Granda
Review DS GA 1002 Statistical and Mathematical Models http://www.cims.nyu.edu/~cfgranda/pages/dsga1002_fall16 Carlos Fernandez-Granda Probability and statistics Probability: Framework for dealing with
More informationSTATS 200: Introduction to Statistical Inference. Lecture 29: Course review
STATS 200: Introduction to Statistical Inference Lecture 29: Course review Course review We started in Lecture 1 with a fundamental assumption: Data is a realization of a random process. The goal throughout
More informationROBUST ESTIMATION OF A CORRELATION COEFFICIENT: AN ATTEMPT OF SURVEY
ROBUST ESTIMATION OF A CORRELATION COEFFICIENT: AN ATTEMPT OF SURVEY G.L. Shevlyakov, P.O. Smirnov St. Petersburg State Polytechnic University St.Petersburg, RUSSIA E-mail: Georgy.Shevlyakov@gmail.com
More informationRegression analysis is a tool for building mathematical and statistical models that characterize relationships between variables Finds a linear
Regression analysis is a tool for building mathematical and statistical models that characterize relationships between variables Finds a linear relationship between: - one independent variable X and -
More informationZwiers FW and Kharin VV Changes in the extremes of the climate simulated by CCC GCM2 under CO 2 doubling. J. Climate 11:
Statistical Analysis of EXTREMES in GEOPHYSICS Zwiers FW and Kharin VV. 1998. Changes in the extremes of the climate simulated by CCC GCM2 under CO 2 doubling. J. Climate 11:2200 2222. http://www.ral.ucar.edu/staff/ericg/readinggroup.html
More informationChapter 1 Statistical Inference
Chapter 1 Statistical Inference causal inference To infer causality, you need a randomized experiment (or a huge observational study and lots of outside information). inference to populations Generalizations
More information3. Tests in the Bernoulli Model
1 of 5 7/29/2009 3:15 PM Virtual Laboratories > 9. Hy pothesis Testing > 1 2 3 4 5 6 7 3. Tests in the Bernoulli Model Preliminaries Suppose that X = (X 1, X 2,..., X n ) is a random sample from the Bernoulli
More informationSmall sample corrections for LTS and MCD
Metrika (2002) 55: 111 123 > Springer-Verlag 2002 Small sample corrections for LTS and MCD G. Pison, S. Van Aelst*, and G. Willems Department of Mathematics and Computer Science, Universitaire Instelling
More informationPackage ForwardSearch
Package ForwardSearch February 19, 2015 Type Package Title Forward Search using asymptotic theory Version 1.0 Date 2014-09-10 Author Bent Nielsen Maintainer Bent Nielsen
More informationFast and robust bootstrap for LTS
Fast and robust bootstrap for LTS Gert Willems a,, Stefan Van Aelst b a Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerp, Belgium b Department of
More informationUQ, Semester 1, 2017, Companion to STAT2201/CIVL2530 Exam Formulae and Tables
UQ, Semester 1, 2017, Companion to STAT2201/CIVL2530 Exam Formulae and Tables To be provided to students with STAT2201 or CIVIL-2530 (Probability and Statistics) Exam Main exam date: Tuesday, 20 June 1
More informationProbability Distribution
Probability Distribution Prof. (Dr.) Rajib Kumar Bhattacharjya Indian Institute of Technology Guwahati Guwahati, Assam Email: rkbc@iitg.ernet.in Web: www.iitg.ernet.in/rkbc Visiting Faculty NIT Meghalaya
More informationDeciding, Estimating, Computing, Checking
Deciding, Estimating, Computing, Checking How are Bayesian posteriors used, computed and validated? Fundamentalist Bayes: The posterior is ALL knowledge you have about the state Use in decision making:
More informationDeciding, Estimating, Computing, Checking. How are Bayesian posteriors used, computed and validated?
Deciding, Estimating, Computing, Checking How are Bayesian posteriors used, computed and validated? Fundamentalist Bayes: The posterior is ALL knowledge you have about the state Use in decision making:
More informationA Test of Cointegration Rank Based Title Component Analysis.
A Test of Cointegration Rank Based Title Component Analysis Author(s) Chigira, Hiroaki Citation Issue 2006-01 Date Type Technical Report Text Version publisher URL http://hdl.handle.net/10086/13683 Right
More informationFundamental Probability and Statistics
Fundamental Probability and Statistics "There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are
More informationStatistical methods and data analysis
Statistical methods and data analysis Teacher Stefano Siboni Aim The aim of the course is to illustrate the basic mathematical tools for the analysis and modelling of experimental data, particularly concerning
More informationA Monte-Carlo study of asymptotically robust tests for correlation coefficients
Biometrika (1973), 6, 3, p. 661 551 Printed in Great Britain A Monte-Carlo study of asymptotically robust tests for correlation coefficients BY G. T. DUNCAN AND M. W. J. LAYAKD University of California,
More informationEXTREMAL QUANTILES OF MAXIMUMS FOR STATIONARY SEQUENCES WITH PSEUDO-STATIONARY TREND WITH APPLICATIONS IN ELECTRICITY CONSUMPTION ALEXANDR V.
MONTENEGRIN STATIONARY JOURNAL TREND WITH OF ECONOMICS, APPLICATIONS Vol. IN 9, ELECTRICITY No. 4 (December CONSUMPTION 2013), 53-63 53 EXTREMAL QUANTILES OF MAXIMUMS FOR STATIONARY SEQUENCES WITH PSEUDO-STATIONARY
More informationBIOL 458 BIOMETRY Lab 9 - Correlation and Bivariate Regression
BIOL 458 BIOMETRY Lab 9 - Correlation and Bivariate Regression Introduction to Correlation and Regression The procedures discussed in the previous ANOVA labs are most useful in cases where we are interested
More informationSection 3: Permutation Inference
Section 3: Permutation Inference Yotam Shem-Tov Fall 2015 Yotam Shem-Tov STAT 239/ PS 236A September 26, 2015 1 / 47 Introduction Throughout this slides we will focus only on randomized experiments, i.e
More informationPERCENTILE ESTIMATES RELATED TO EXPONENTIAL AND PARETO DISTRIBUTIONS
PERCENTILE ESTIMATES RELATED TO EXPONENTIAL AND PARETO DISTRIBUTIONS INTRODUCTION The paper as posted to my website examined percentile statistics from a parent-offspring or Neyman- Scott spatial pattern.
More informationLec 3: Model Adequacy Checking
November 16, 2011 Model validation Model validation is a very important step in the model building procedure. (one of the most overlooked) A high R 2 value does not guarantee that the model fits the data
More informationA nonparametric test for trend based on initial ranks
Journal of Statistical Computation and Simulation Vol. 76, No. 9, September 006, 89 837 A nonparametric test for trend based on initial ranks GLENN HOFMANN* and N. BALAKRISHNAN HSBC, USA ID Analytics,
More informationCOMPARISON OF THE ESTIMATORS OF THE LOCATION AND SCALE PARAMETERS UNDER THE MIXTURE AND OUTLIER MODELS VIA SIMULATION
(REFEREED RESEARCH) COMPARISON OF THE ESTIMATORS OF THE LOCATION AND SCALE PARAMETERS UNDER THE MIXTURE AND OUTLIER MODELS VIA SIMULATION Hakan S. Sazak 1, *, Hülya Yılmaz 2 1 Ege University, Department
More informationSimulating Uniform- and Triangular- Based Double Power Method Distributions
Journal of Statistical and Econometric Methods, vol.6, no.1, 2017, 1-44 ISSN: 1792-6602 (print), 1792-6939 (online) Scienpress Ltd, 2017 Simulating Uniform- and Triangular- Based Double Power Method Distributions
More informationSome Monte Carlo Evidence for Adaptive Estimation of Unit-Time Varying Heteroscedastic Panel Data Models
Some Monte Carlo Evidence for Adaptive Estimation of Unit-Time Varying Heteroscedastic Panel Data Models G. R. Pasha Department of Statistics, Bahauddin Zakariya University Multan, Pakistan E-mail: drpasha@bzu.edu.pk
More informationDistribution Theory. Comparison Between Two Quantiles: The Normal and Exponential Cases
Communications in Statistics Simulation and Computation, 34: 43 5, 005 Copyright Taylor & Francis, Inc. ISSN: 0361-0918 print/153-4141 online DOI: 10.1081/SAC-00055639 Distribution Theory Comparison Between
More informationSUPPLEMENT TO PARAMETRIC OR NONPARAMETRIC? A PARAMETRICNESS INDEX FOR MODEL SELECTION. University of Minnesota
Submitted to the Annals of Statistics arxiv: math.pr/0000000 SUPPLEMENT TO PARAMETRIC OR NONPARAMETRIC? A PARAMETRICNESS INDEX FOR MODEL SELECTION By Wei Liu and Yuhong Yang University of Minnesota In
More informationApplication of Variance Homogeneity Tests Under Violation of Normality Assumption
Application of Variance Homogeneity Tests Under Violation of Normality Assumption Alisa A. Gorbunova, Boris Yu. Lemeshko Novosibirsk State Technical University Novosibirsk, Russia e-mail: gorbunova.alisa@gmail.com
More informationApplication of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption
Application of Parametric Homogeneity of Variances Tests under Violation of Classical Assumption Alisa A. Gorbunova and Boris Yu. Lemeshko Novosibirsk State Technical University Department of Applied Mathematics,
More informationIntroduction to Algorithmic Trading Strategies Lecture 10
Introduction to Algorithmic Trading Strategies Lecture 10 Risk Management Haksun Li haksun.li@numericalmethod.com www.numericalmethod.com Outline Value at Risk (VaR) Extreme Value Theory (EVT) References
More informationThe Model Building Process Part I: Checking Model Assumptions Best Practice
The Model Building Process Part I: Checking Model Assumptions Best Practice Authored by: Sarah Burke, PhD 31 July 2017 The goal of the STAT T&E COE is to assist in developing rigorous, defensible test
More informationCHAPTER 5. Outlier Detection in Multivariate Data
CHAPTER 5 Outlier Detection in Multivariate Data 5.1 Introduction Multivariate outlier detection is the important task of statistical analysis of multivariate data. Many methods have been proposed for
More informationMedian Cross-Validation
Median Cross-Validation Chi-Wai Yu 1, and Bertrand Clarke 2 1 Department of Mathematics Hong Kong University of Science and Technology 2 Department of Medicine University of Miami IISA 2011 Outline Motivational
More informationA comparison study of the nonparametric tests based on the empirical distributions
통계연구 (2015), 제 20 권제 3 호, 1-12 A comparison study of the nonparametric tests based on the empirical distributions Hyo-Il Park 1) Abstract In this study, we propose a nonparametric test based on the empirical
More informationComputational Statistics and Data Analysis
Computational Statistics and Data Analysis 54 (2010) 3300 3312 Contents lists available at ScienceDirect Computational Statistics and Data Analysis journal homepage: www.elsevier.com/locate/csda Robust
More informationBasics of Experimental Design. Review of Statistics. Basic Study. Experimental Design. When an Experiment is Not Possible. Studying Relations
Basics of Experimental Design Review of Statistics And Experimental Design Scientists study relation between variables In the context of experiments these variables are called independent and dependent
More information2. TRUE or FALSE: Converting the units of one measured variable alters the correlation of between it and a second variable.
1. The diagnostic plots shown below are from a linear regression that models a patient s score from the SUG-HIGH diabetes risk model as function of their normalized LDL level. a. Based on these plots,
More informationUniversity of Lisbon, Portugal
Development and comparative study of two near-exact approximations to the distribution of the product of an odd number of independent Beta random variables Luís M. Grilo a,, Carlos A. Coelho b, a Dep.
More informationTesting for a unit root in an ar(1) model using three and four moment approximations: symmetric distributions
Hong Kong Baptist University HKBU Institutional Repository Department of Economics Journal Articles Department of Economics 1998 Testing for a unit root in an ar(1) model using three and four moment approximations:
More informationThe Model Building Process Part I: Checking Model Assumptions Best Practice (Version 1.1)
The Model Building Process Part I: Checking Model Assumptions Best Practice (Version 1.1) Authored by: Sarah Burke, PhD Version 1: 31 July 2017 Version 1.1: 24 October 2017 The goal of the STAT T&E COE
More informationTesting for Regime Switching in Singaporean Business Cycles
Testing for Regime Switching in Singaporean Business Cycles Robert Breunig School of Economics Faculty of Economics and Commerce Australian National University and Alison Stegman Research School of Pacific
More informationTentative solutions TMA4255 Applied Statistics 16 May, 2015
Norwegian University of Science and Technology Department of Mathematical Sciences Page of 9 Tentative solutions TMA455 Applied Statistics 6 May, 05 Problem Manufacturer of fertilizers a) Are these independent
More informationIMPROVING THE SMALL-SAMPLE EFFICIENCY OF A ROBUST CORRELATION MATRIX: A NOTE
IMPROVING THE SMALL-SAMPLE EFFICIENCY OF A ROBUST CORRELATION MATRIX: A NOTE Eric Blankmeyer Department of Finance and Economics McCoy College of Business Administration Texas State University San Marcos
More informationResearch Note: A more powerful test statistic for reasoning about interference between units
Research Note: A more powerful test statistic for reasoning about interference between units Jake Bowers Mark Fredrickson Peter M. Aronow August 26, 2015 Abstract Bowers, Fredrickson and Panagopoulos (2012)
More informationRegression Diagnostics for Survey Data
Regression Diagnostics for Survey Data Richard Valliant Joint Program in Survey Methodology, University of Maryland and University of Michigan USA Jianzhu Li (Westat), Dan Liao (JPSM) 1 Introduction Topics
More informationRISK AND EXTREMES: ASSESSING THE PROBABILITIES OF VERY RARE EVENTS
RISK AND EXTREMES: ASSESSING THE PROBABILITIES OF VERY RARE EVENTS Richard L. Smith Department of Statistics and Operations Research University of North Carolina Chapel Hill, NC 27599-3260 rls@email.unc.edu
More informationA Large Sample Normality Test
Faculty Working Paper 93-0171 330 STX B385 1993:171 COPY 2 A Large Sample Normality Test ^' of the JAN /> -, ^'^^srsitv fj nil, Anil K. Bera Pin T. Ng Department of Economics Department of Economics University
More informationON SMALL SAMPLE PROPERTIES OF PERMUTATION TESTS: INDEPENDENCE BETWEEN TWO SAMPLES
ON SMALL SAMPLE PROPERTIES OF PERMUTATION TESTS: INDEPENDENCE BETWEEN TWO SAMPLES Hisashi Tanizaki Graduate School of Economics, Kobe University, Kobe 657-8501, Japan e-mail: tanizaki@kobe-u.ac.jp Abstract:
More informationOne-Sample Numerical Data
One-Sample Numerical Data quantiles, boxplot, histogram, bootstrap confidence intervals, goodness-of-fit tests University of California, San Diego Instructor: Ery Arias-Castro http://math.ucsd.edu/~eariasca/teaching.html
More informationSubject CS1 Actuarial Statistics 1 Core Principles
Institute of Actuaries of India Subject CS1 Actuarial Statistics 1 Core Principles For 2019 Examinations Aim The aim of the Actuarial Statistics 1 subject is to provide a grounding in mathematical and
More informationINVERTED KUMARASWAMY DISTRIBUTION: PROPERTIES AND ESTIMATION
Pak. J. Statist. 2017 Vol. 33(1), 37-61 INVERTED KUMARASWAMY DISTRIBUTION: PROPERTIES AND ESTIMATION A. M. Abd AL-Fattah, A.A. EL-Helbawy G.R. AL-Dayian Statistics Department, Faculty of Commerce, AL-Azhar
More information